Question

Can anyone help me with this? I will give you a shiny medal :) Please give detailed instructions :>

If Sinθ = 3/5 and 0≤ θ ≤π/2, then tan θ = to what?
I'm not sure what to do so please give me detailed instructions, thank you :)

Answer 1

I do know that tan is opposite/adjacent? But I'm not sure how to deal with the inequality :,<

Answer 2

The inequality just tells you what quadrant the angle is in (you only need to know it, to know if tan θ is positive or negative)

Use Sinθ = 3/5 to draw a right triangle,
since sinθ = opposite/hyptenuse.

Answer 3

so how exactly do I find the adjacent length? It will be 3/x tan?

Answer 4

\[\frac{ 3 }{ x }\tan^{-1} \]

Answer 5

No. Use pythag.

Answer 6

ooh a^2+b^2 = c^2?

Answer 7

so its: \[3^2 + b^2 = 5^2\]

Answer 8

Which then becomes 9 + b^2 = 25 so I subtract 9 to 25 so I get B^2= 16

Answer 9

so x = 4 because the 4(4) = 16?

Answer 10

so it's tanθ = 3/4

Answer 11

Yep.

Answer 12

aww thank you so much! :D

Answer 13

But don't forget, which quadrant is this?
0≤ θ ≤π/2

And is tan positive or negative in that quadrant?

Answer 14

I'm not really sure to be honest

Answer 15

it would be positive right? Im guessing? because:

Answer 16

Is that correct or no?

Answer 17

Not quite.

This shows the angles (make sure you know this)
http://thepythongamebook.com/_media/en:part2:600px-unit_circle_angles.svg-kleiner.png

This show whether positive or negative http://cdn-3.ask-math.com/images/astc-rule-in-trigonometry.png

Answer 18

Ohh, I really screwed up on my drawing then oops so it would be positive because tan and cot are positive right? :D

Answer 19

Which quadrant is this?
0 ≤ θ ≤ π/2

Answer 20

and since its less than or equal to pi/2 that means its positive as well :D?

Answer 21

that quadrant is quadrant I right?

Answer 22

Yep

Answer 23

wow!! Omigosh, thank you so much for teaching me and helping me with this problem! I learned a lot!

Answer 24

My teachers didn't help me like that xD q-q

Answer 25

Welcome. Don't forget that they're all positive in quadrant 1.

Probably cos not all math teachers really know math ;P

Answer 26

Welcome :)

Answer 27

:D

Answer 28

:D